I am trying to understand what work really means in physics. I seem to be missing the conceptual link. Every resource says that $W=Fd$ but that does not make sense to me.
If, say, an elastic object suspended in space where there is no drag or resisting force of any kind is pushed by a force of a certain magnitude, then it will accelerate. The amount of 'useful' energy spent would completely go into accelerating this body of a particular mass for as long as the force is applied.
First of all, why isn't work $W = mat$ (which is the equation of momentum) for some time $t$.
Why is work $W = mas$ (for a force acting in the same direction of the motion) for some displacement $s$.
Since momentum and energy are both conserved, could it have been that it was a matter of convention how these two quantities were defined? (I.e why wasn't work defined as $W=mat$)?